IODS course project
Aleksandra Konovalova
About the project
I am looking forward to get more first-hand experience with R and data visualization and analysis.
My GitHub:
https://github.com/AleksanKo/IODS-project
Regression and model validation
I have completed the data wrangling exercises: I’ve read the data from the file with the help of read.csv function, created a new dataset by taking columns from the old one and written it to a new file (write.csv).
Logistic regression
I have completed the data wrangling exercises: I’ve read the data from the file with the help of read.csv function, created a new dataset by taking columns from the old one and written it to a new file (write.csv).
Data description
matpor <- read.csv("http://s3.amazonaws.com/assets.datacamp.com/production/course_2218/datasets/alc.txt", sep=',')
colnames(matpor)## [1] "school" "sex" "age" "address" "famsize" "Pstatus"
## [7] "Medu" "Fedu" "Mjob" "Fjob" "reason" "nursery"
## [13] "internet" "guardian" "traveltime" "studytime" "failures" "schoolsup"
## [19] "famsup" "paid" "activities" "higher" "romantic" "famrel"
## [25] "freetime" "goout" "Dalc" "Walc" "health" "absences"
## [31] "G1" "G2" "G3" "alc_use" "high_use"The dataset consists of 35 variables. Many factors has only two levels and are thus binary. Such factors include:
- school (student’s school: ‘GP’ = Gabriel Pereira,‘MS’ = Mousinho da Silveira)
- sex (‘F’ = female, ‘M’ = male)
- address (where does the student live: ‘U’ = urban area, ‘R’ = rural area)
- famsize (the number of family members: ‘LE3’ - less or equal to 3 family members, ‘GT3’ - greater than 3 family members))
- Pstatus (whether the student’s parents are living together or not: ‘T’ - living together, ‘A’ - living apart)
- nursery (if the student went to nursery school: yes/no)
- internet (if the student has an Internet access at home: yes/no)
- schoolsup (if the student gets extra educational support: yes/no)
- famsup (if the student gets family educational support: yes/no)
- paid (if the student has extra paid classes within the course subject (Math or Portuguese): yes/no)
- activities (if the student has extra-curricular activities: yes/no)
- higher (if the student wants to take higher education: yes/no)
- romantic (if the student is in a romantic relationship: yes/no)
Other factor variables include:
- Mjob (mother’s job: ‘teacher’, ‘health’, ‘services’ (e.g. administrative or police), ‘at_home’, ‘other’)
- Fjob (father’s job: same levels as Mjob)
- reason (the student’s reason to choose this school: ‘home’,‘reputation’, ‘course’, ‘other’)
- guardian (the student’s guardian: ‘mother’, ‘father’, ‘other’)
Integer variables include (if it ranges from 1 to 5, it is a range between “very bad”/“very low” and “excellent”/“very high”):
- age
- Medu (mother’s education: 0 - none, 1 - primary education (4th grade), 2 - 5th to 9th grade, 3 - secondary education, 4 - higher education)
- Fedu (father’s education: same levels as Medu)
- traveltime (home to school travel time: 1 - <15 min., 2 - 15 to 30 min., 3 - 30 min. to 1 hour, 4 - >1 hour)
- studytime (weekly study time: 1 - <2 hours, 2 - 2 to 5 hours, 3 - 5 to 10 hours, 4 - >10 hours)
- failures
- famrel (quality of family relationships: from 1 to 5)
- freetime (free time after school: from 1 to 5)
- goout (going out with friends: from 1 to 5)
- Dalc (workday alcohol consumption: from 1 to 5)
- Walc (weekend alcohol consumption: from 1 to 5)
- health (current health status: from 1 to 5)
- absences
- G1 (first period grade)
- G2 (second period grade)
- G3 (final grade)
- alc_use (average use of alcohol during the week)
There is also a logical variable high_use which shows if the average alcohol consumption is high (more than 2) or not.
Hypotheses
I have chosen 4 variables: activities, famrel, higher and internet. My hypotheses for them are following:
- Having extra-curricular activities correlates with low alcohol consumption.
- Having good (from 3 to 5) family relationships correlates with low alcohol consumption.
- Wish to get a higher education correlates with low alcohol consumption.
- Having Internet connection at home correlates with low alcohol consumption.
Plots
Plot for Hypothesis 1: 
It seems that there are more students with high alcohol consumption amongst those who don’t have any activities. However, the data shows (both visually and mathematically) that the number of students who have a high alcohol consumption is almost the same:
n1<-nrow(filter(matpor,activities=="yes",high_use==TRUE))
n2<-nrow(filter(matpor,activities=="no",high_use==TRUE))The difference between low alcohol consumption of the active and non-active students is also not so significant:
n3<-nrow(filter(matpor,activities=="yes",high_use==FALSE))
n4<-nrow(filter(matpor,activities=="no",high_use==FALSE))Plot for Hypothesis 2: 
It seems like most of the students ranked their family relationships as good or excellent (>250 students) which makes further analysis difficult. However, it is worth noting that the maximal amount of students with a hish alcohol consumption comes from a family with good internal relationships.
Plot for Hypothesis 3: 
There is also no correlation between striving to get a higher education and alcohol consumption, sinse almost every student wants to get a higher education.
Plot for Hypothesis 4: 
Almost the same results as for Hypothesis 1: there seems no correlation between having Internet and alcohol consumption. Only 15 students who don’t have Internet at home drink alcohol a lot, but there are 97 who drink a lot of alcohol and have Internet. However, if we count the percentage, it turns out that 26% of those without Internet drink alcohol and the corresponding amount of the students with Internet is 30%. The same filter (as in Hypothesis 1) was used to count the numbers:
i<-nrow(filter(matpor,internet=="yes",high_use==TRUE))Logistic regression model
m <- glm(high_use ~ activities + famrel + internet + higher, data = matpor, family = "binomial")
summary(m)##
## Call:
## glm(formula = high_use ~ activities + famrel + internet + higher,
## family = "binomial", data = matpor)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.3167 -0.8643 -0.7642 1.3863 1.8870
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.9163 0.7070 1.296 0.1950
## activitiesyes -0.2410 0.2302 -1.047 0.2952
## famrel -0.2893 0.1213 -2.385 0.0171 *
## internetyes 0.2733 0.3297 0.829 0.4071
## higheryes -0.8244 0.4939 -1.669 0.0951 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 462.21 on 381 degrees of freedom
## Residual deviance: 451.26 on 377 degrees of freedom
## AIC: 461.26
##
## Number of Fisher Scoring iterations: 4coef(m)## (Intercept) activitiesyes famrel internetyes higheryes
## 0.9162589 -0.2409905 -0.2893345 0.2732788 -0.8244081OR <- exp(coef(m))
OR## (Intercept) activitiesyes famrel internetyes higheryes
## 2.4999204 0.7858491 0.7487617 1.3142666 0.4384945- Each one-unit change in famrel makes high_use less likely by 28.9%
- If the student has any activities, the possibility that he has high alcohol consumption is reduced by 24%
- If the student is planning to get a higher education, the possibility that he has high alcohol consumption is reduced by 82%
- If the student has internet at home, then the odds of him/her drinking a lot is increased by 27.3%
Probabilities
## prediction
## high_use FALSE TRUE
## FALSE 258 10
## TRUE 109 5
The prediction is wrong in 119 cases. Only 5 cases are true positive as TRUE, but 258 cases are true positive as FALSE.
loss_func <- function(class, prob) {
n_wrong <- abs(class - prob) > 0.5
mean(n_wrong)
}
loss_func(alc$high_use,alc$probability)## [1] 0.3115183library(boot)
cv <- cv.glm(data = alc, cost = loss_func, glmfit = m, K = 10)
cv$delta[1]## [1] 0.3089005The number of the wrong predictions on the testing data is the same as on the traning data.
Clustering and classification
Data wrangling exercises are done in the corresponding R script.
Analysis exercises
Firstly, the Boston dataset is loaded from the MASS package:
library(MASS)
library(dplyr)
data(Boston)
str(Boston)## 'data.frame': 506 obs. of 14 variables:
## $ crim : num 0.00632 0.02731 0.02729 0.03237 0.06905 ...
## $ zn : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
## $ indus : num 2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
## $ chas : int 0 0 0 0 0 0 0 0 0 0 ...
## $ nox : num 0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
## $ rm : num 6.58 6.42 7.18 7 7.15 ...
## $ age : num 65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
## $ dis : num 4.09 4.97 4.97 6.06 6.06 ...
## $ rad : int 1 2 2 3 3 3 5 5 5 5 ...
## $ tax : num 296 242 242 222 222 222 311 311 311 311 ...
## $ ptratio: num 15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
## $ black : num 397 397 393 395 397 ...
## $ lstat : num 4.98 9.14 4.03 2.94 5.33 ...
## $ medv : num 24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...dim(Boston)## [1] 506 14The data has 14 variables, all of them are either numeric or integer. Variables include e.g. crime rate by town per capita (crim), nitrogen oxides concentration (nox), index of accessibility to radial highways (rad), pupil-teacher ratio by town (ptratio), average number of rooms per dwelling (rm) and others.
summary(Boston)## crim zn indus chas nox
## Min. : 0.00632 Min. : 0.00 Min. : 0.46 Min. :0.00000 Min. :0.3850
## 1st Qu.: 0.08204 1st Qu.: 0.00 1st Qu.: 5.19 1st Qu.:0.00000 1st Qu.:0.4490
## Median : 0.25651 Median : 0.00 Median : 9.69 Median :0.00000 Median :0.5380
## Mean : 3.61352 Mean : 11.36 Mean :11.14 Mean :0.06917 Mean :0.5547
## 3rd Qu.: 3.67708 3rd Qu.: 12.50 3rd Qu.:18.10 3rd Qu.:0.00000 3rd Qu.:0.6240
## Max. :88.97620 Max. :100.00 Max. :27.74 Max. :1.00000 Max. :0.8710
## rm age dis rad tax
## Min. :3.561 Min. : 2.90 Min. : 1.130 Min. : 1.000 Min. :187.0
## 1st Qu.:5.886 1st Qu.: 45.02 1st Qu.: 2.100 1st Qu.: 4.000 1st Qu.:279.0
## Median :6.208 Median : 77.50 Median : 3.207 Median : 5.000 Median :330.0
## Mean :6.285 Mean : 68.57 Mean : 3.795 Mean : 9.549 Mean :408.2
## 3rd Qu.:6.623 3rd Qu.: 94.08 3rd Qu.: 5.188 3rd Qu.:24.000 3rd Qu.:666.0
## Max. :8.780 Max. :100.00 Max. :12.127 Max. :24.000 Max. :711.0
## ptratio black lstat medv
## Min. :12.60 Min. : 0.32 Min. : 1.73 Min. : 5.00
## 1st Qu.:17.40 1st Qu.:375.38 1st Qu.: 6.95 1st Qu.:17.02
## Median :19.05 Median :391.44 Median :11.36 Median :21.20
## Mean :18.46 Mean :356.67 Mean :12.65 Mean :22.53
## 3rd Qu.:20.20 3rd Qu.:396.23 3rd Qu.:16.95 3rd Qu.:25.00
## Max. :22.00 Max. :396.90 Max. :37.97 Max. :50.00rad (index of accessibility ro radial highways) varies from 1 to 24. lstat (lower status of the population (in percents)) has several outliers: min lstat is 1.73%, max lstat is 37.97 %, and the mean is 12.65%. There is also a noticeable outlier in crim variable: max crim = 87.98. An outlier is also present in black variable (1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town): min black = 0.32.
pairs(Boston)
There is a clear hyperbolic relationship between nox and dis (weighted mean of distances to five Boston employment centres) variables: the more the concentration of nitrogen oxides, the less the weighted mean of distances to employment centers. Thus, we can say that there is a correlation between nitrogen oxides and employments centers.
There is also a hyperbolic relationship between lstat and medv (median value of owner-occupied homes in $1000s) variables: the lower the status of the population, the less the median cost of the homes in the area, which is pretty logical.
There is almost a linear correlation between rm (average number of rooms per dwelling) and lstat variables: the more rooms in the dwelling, the more the median cost of the homes and vice versa.
Now the dataset will be standardized and a new variable will be added to the dataset (the old variable crim will be dropped):
boston_scaled <- scale(Boston)
summary(boston_scaled)## crim zn indus chas
## Min. :-0.419367 Min. :-0.48724 Min. :-1.5563 Min. :-0.2723
## 1st Qu.:-0.410563 1st Qu.:-0.48724 1st Qu.:-0.8668 1st Qu.:-0.2723
## Median :-0.390280 Median :-0.48724 Median :-0.2109 Median :-0.2723
## Mean : 0.000000 Mean : 0.00000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.007389 3rd Qu.: 0.04872 3rd Qu.: 1.0150 3rd Qu.:-0.2723
## Max. : 9.924110 Max. : 3.80047 Max. : 2.4202 Max. : 3.6648
## nox rm age dis
## Min. :-1.4644 Min. :-3.8764 Min. :-2.3331 Min. :-1.2658
## 1st Qu.:-0.9121 1st Qu.:-0.5681 1st Qu.:-0.8366 1st Qu.:-0.8049
## Median :-0.1441 Median :-0.1084 Median : 0.3171 Median :-0.2790
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.5981 3rd Qu.: 0.4823 3rd Qu.: 0.9059 3rd Qu.: 0.6617
## Max. : 2.7296 Max. : 3.5515 Max. : 1.1164 Max. : 3.9566
## rad tax ptratio black
## Min. :-0.9819 Min. :-1.3127 Min. :-2.7047 Min. :-3.9033
## 1st Qu.:-0.6373 1st Qu.:-0.7668 1st Qu.:-0.4876 1st Qu.: 0.2049
## Median :-0.5225 Median :-0.4642 Median : 0.2746 Median : 0.3808
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 1.6596 3rd Qu.: 1.5294 3rd Qu.: 0.8058 3rd Qu.: 0.4332
## Max. : 1.6596 Max. : 1.7964 Max. : 1.6372 Max. : 0.4406
## lstat medv
## Min. :-1.5296 Min. :-1.9063
## 1st Qu.:-0.7986 1st Qu.:-0.5989
## Median :-0.1811 Median :-0.1449
## Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.6024 3rd Qu.: 0.2683
## Max. : 3.5453 Max. : 2.9865boston_scaled <- as.data.frame(boston_scaled)
summary(boston_scaled$crim)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.419367 -0.410563 -0.390280 0.000000 0.007389 9.924110#creating a new variable
breakpoints <- quantile(boston_scaled$crim)
labels <- c('low','med_low','med_high','high')
crime <- cut(boston_scaled$crim, breaks = breakpoints, include.lowest = TRUE, label=labels)
#dropping and adding variables
boston_scaled <- dplyr::select(boston_scaled, -crim)
boston_scaled <- data.frame(boston_scaled, crime)Diving the data to train and test data:
n <- nrow(boston_scaled)
random_rows <- sample(n, size = n * 0.8)
train_data <- boston_scaled[random_rows,]
test_data <- boston_scaled[-random_rows,]Linear discriminant analysis
Fitting and plotting the LDA:
lda.fit <- lda(crime ~ ., data = train_data)
classes <- as.numeric(train_data$crime)
plot(lda.fit, dimen = 2,col=classes,pch=classes)
Predicting the classes with the LDA model:
correct_classes <- test_data[,"crime"]
test_data <- dplyr::select(test_data, -crime)
lda.pred <- predict(lda.fit, newdata = test_data)
table(correct = correct_classes, predicted = lda.pred$class)## predicted
## correct low med_low med_high high
## low 22 5 1 0
## med_low 6 13 8 0
## med_high 0 5 17 0
## high 0 0 0 25Overall results show that high crime rate was predicted correctly (there is only one case when medium high crime rate was predicted wrong as high). Low crime rate was predicted correctly for 17 cases, for 13 cases it was predicted as med_low and for 2 - as med_high. Medium low crime rate was predicted correctly 15 times with only 6 errors.
Calculating the distances and visualizing the clusters:
library(MASS)
data('Boston')
boston_scaled_again <- scale(Boston)
dist_eu <- dist(boston_scaled_again)
km <-kmeans(Boston, centers = 2)
pairs(Boston, col = km$cluster)
The optimal number of clusters is 2: 3 look good already, but one of them (the black one) doesn’t seem to be of great significance. More than 3 clusters is abundant. In case of rad, tax and ptratio the red cluster clearly shows outliers. There are overlapping clusters in lstat and medv plot: one is corresponding to the bigger amount of people who are of lower status and to the smaller median cost of homes, and the other is corresponding to the bigger amount of people with higher status and to bigger median cost of homes (basically, it is poverty vs richness dichotomy)
Bonus Task:
model_predictors <- dplyr::select(train_data, -crime)
# check the dimensions
dim(model_predictors)## [1] 404 13dim(lda.fit$scaling)## [1] 13 3# matrix multiplication
matrix_product <- as.matrix(model_predictors) %*% lda.fit$scaling
matrix_product <- as.data.frame(matrix_product)
install.packages("plotly")## Error in install.packages : Updating loaded packageslibrary("plotly")
#colors from the crime classes
plot_ly(x = matrix_product$LD1, y = matrix_product$LD2, z = matrix_product$LD3, type= 'scatter3d', mode='markers',color=train_data$crime)